Flow-induced vibrations and the Landau equation

Abstract

The initial and general transient temporal behaviours of flow induced vibrations were studied particularly with regard to the extent with which self-excited, flow-induced vibrations can be described by the Landau equation.Three different cases are studied experimentally, using bodies with generic shape. The first case represents a bluff body: resembling a simplified section of the Tacoma bridge, which has a single torsional degree of freedom. The second case is a two-dimensional airfoil in transonic flow having a heave and a torsional degree of freedom. The third case is an elastic half-wing model, also investigated in transonic flow.It is shown that in all three cases, beyond the critical point and at small initial amplitude the temporal development of the oscillations up to the limit cycle i.e. the envelope of the measured time functions, agrees with the corresponding curve, given by the solution of the Landau equation. For the Tacoma section and the airfoil the same agreement was demonstrated for initial amplitudes much larger than that of the limit cycle. In addition for both last cases the bifurcation behaviour was investigated and the Landau constants were determined. Finally an elementary physical explanation for the instability phenomenon was given.